* Senior club appearances and goals counted for the domestic league only and correct as of 14:20, 5 May 2019‡ National team caps and goals correct as of 26 March 2019

He began his career with KTP and moved to Sevilla in 2008, where he played only one La Liga game for the first team before returning to Finland with HJK. He then played in the top divisions of Germany for Schalke 04, Scotland for Celtic and Denmark for Brøndby. In 2018 he signed for Norwich City on a free transfer and was named player of the season in the 2018–19 EFL Championship. Pukki made his international debut for Finland in 2009 and has earned 70 caps, scoring 15 goals.

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Pukki began his football career in childhood in HOPS (Hovinsaaren Palloseura) while living in Hovinsaari, Kotka. As a youth he joint his official hometown club, KTP, playing for their under-19 side. He made his debut for the first team at 16 years old and his performances saw him called up to play for Finland's youth international sides.[1][2] In two seasons of first-team football, Pukki made 29 appearances in the Finnish Premier League (Veikkausliiga) and scored three goals.[2]

Pukki moved to Sevilla from KTP[2] and was called up for the Sevilla first team for the away match against Real Madrid on 7 December 2008,[3] but was an unused substitute. He received his La Liga debut at home against Racing on 25 January 2009.[4] He found himself unused in Sevilla playing mostly for the reserve side Sevilla Atletico and he decided to return to Finland.

On 28 August 2010, Pukki signed a three-and-half-year contract with the Finnish Veikkausliiga club HJK.[5] Pukki made his debut 30 August a match against IFK Mariehamn. He managed to score his first goal for HJK in the next match against FF Jaro which was his first goal in a league match for nearly two years. During season 2010 he managed to play in seven games and score two goals for HJK in the 2010 season. At the end of the season HJK and Pukki won the Finnish Veikkausliiga and silver in the Finnish Cup.

During season 2011 he scored 11 goals and notched eight assists in 18 league matches out which he was in the starting line up in 13. He was chosen to 2011 Veikkausliiga All Stars -team.[6] Pukki was also a key figure in HJK´s UEFA Champions League and UEFA Europa League qualifications. He scored two goals against Bangor City and HJK´s both goals in a 2–0 home win against FC Schalke 04.[7] Pukki also scored HJK´s only goal in the 6–1 away match against Schalke.[8]

Pukki scored three goals in two matches against FC Schalke 04 in August 2011 during the Europa League qualifier. First he scored twice in the first leg in Helsinki, and in Gelsenkirchen he scored an away goal. However, it was not enough to help HJK qualify to the group stage. On 31 August 2011, Pukki joined Schalke on a three-year contract.[9]

On 6 November, he scored two goals for Schalke as he debuted in the starting 11 against Hannover 96. By doing so, he became the third Finn to score a brace in the German Bundesliga, after Ari Hjelm and Pasi Rautiainen.[10]

Pukki signed a four-year deal with Celtic from FC Schalke 04 for an undisclosed fee on 31 August 2013.[11] He scored on his debut in a 3–1 win against Hearts on 14 September 2013[12] and again on his home debut against St Johnstone on 21 September. On 26 January 2014 he scored against Hibernian.[13] Overall though, Pukki's first season at Celtic was considered something of a disappointment as he struggled with form and failed to fill the void left by Gary Hooper who had left at the start of the season.[14][15] Pukki himself later acknowledged the lack of impact he had made, admitting he initially felt playing in Scotland would be "easier" than in Germany.[16] He found the speed and physical nature of the game in Scotland difficult to adjust to, and stated "Scottish football is not easy. It’s not a bad league at all".[16]

On 1 September 2014, Pukki signed a one-year loan deal with option to buy with Danish side Brøndby IF.[18] He made his debut 13 days later in a league match at home against Randers[20] and scored his first goal two weeks later in a 2–2 draw away against Esbjerg.[20] He went on to score another four goals in his next four games,[20][21] and was rewarded for his form by being voted the Superliga Player of the Month for October,[22] finishing the season as the club's top scorer, with nine goals.[23] On 19 June 2015, Pukki signed a three-year contract with Brøndby for an undisclosed fee.[23] On 4 August 2016, Pukki scored three goals when Brøndby knocked out Hertha BSC in the third round of the 2016–17 UEFA Europa League qualifiers, winning 3–1, thereby overcoming a 0–1 deficit from the first leg in Berlin.[24]

From January to February 2019, Pukki scored eight goals across six consecutive matches, ending with two goals in a 4–0 win at Bolton Wanderers.[32] This run included two goals on 10 February in a 3–0 win over Ipswich Town in the Old Farm derby, with which he became the Finn with the most goals in a Championship season, overtaking former Ipswich player Shefki Kuqi's 20 in 2004–05.[33]

In April 2019, Pukki was named EFL Championship Player of the Season and was included in the 2018–19 Championship Team of the Season.[34][35] He was also named Norwich City F.C. Player of the Season by Norwich City's supporters for 2018–19 and received the Barry Butler Memorial Trophy.